Average Error: 15.7 → 1.2
Time: 6.4s
Precision: 64
\[\sqrt[3]{\frac{g}{2 \cdot a}}\]
↓
\[\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]
\sqrt[3]{\frac{g}{2 \cdot a}}
↓
\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}
double f(double g, double a) {
        double r135746 = g;
        double r135747 = 2.0;
        double r135748 = a;
        double r135749 = r135747 * r135748;
        double r135750 = r135746 / r135749;
        double r135751 = cbrt(r135750);
        return r135751;
}
↓
double f(double g, double a) {
        double r135752 = g;
        double r135753 = cbrt(r135752);
        double r135754 = r135753 * r135753;
        double r135755 = 2.0;
        double r135756 = r135754 / r135755;
        double r135757 = cbrt(r135756);
        double r135758 = sqrt(r135757);
        double r135759 = r135758 * r135758;
        double r135760 = cbrt(r135753);
        double r135761 = a;
        double r135762 = cbrt(r135761);
        double r135763 = r135760 / r135762;
        double r135764 = r135759 * r135763;
        return r135764;
}

Error

Bits error versus g

Bits error versus a

Try it out

Your Program's Arguments

Results

Enter valid numbers for all inputs

Derivation

  1. Initial program 15.7

    \[\sqrt[3]{\frac{g}{2 \cdot a}}\]
  2. Using strategy rm

  3. Applied add-cube-cbrt15.9

    \[\leadsto \sqrt[3]{\frac{\color{blue}{\left(\sqrt[3]{g} \cdot \sqrt[3]{g}\right) \cdot \sqrt[3]{g}}}{2 \cdot a}}\]

  4. Applied times-frac15.9

    \[\leadsto \sqrt[3]{\color{blue}{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2} \cdot \frac{\sqrt[3]{g}}{a}}}\]

  5. Applied cbrt-prod5.9

    \[\leadsto \color{blue}{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \sqrt[3]{\frac{\sqrt[3]{g}}{a}}}\]
  6. Using strategy rm

  7. Applied cbrt-div1.1

    \[\leadsto \sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}} \cdot \color{blue}{\frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}}\]
  8. Using strategy rm

  9. Applied add-sqr-sqrt1.2

    \[\leadsto \color{blue}{\left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right)} \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]

  10. Final simplification1.2

    \[\leadsto \left(\sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}} \cdot \sqrt{\sqrt[3]{\frac{\sqrt[3]{g} \cdot \sqrt[3]{g}}{2}}}\right) \cdot \frac{\sqrt[3]{\sqrt[3]{g}}}{\sqrt[3]{a}}\]

Reproduce

herbie shell --seed 2020062 
(FPCore (g a)
  :name "2-ancestry mixing, zero discriminant"
  :precision binary64
  (cbrt (/ g (* 2 a))))